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Emerging Flux Simulations& semi-Sunspots

Bob SteinA. LagerfjärdÅ. Nordlund

D. Georgobiani

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Objectives

• Complement Flux Emergence Simulations of coherent, twisted flux tubes by using minimally structured field -> horizontal, uniform, untwisted in inflows at bottom

• Investigate formation and structure of sunspots• Provide synthetic data for validating local

helioseismology and vector magnetograph inversion procedures

• Investigate nature of supergranulation

Numerical Method• Spatial differencing

– 6th-order finite difference– staggered (5th order interpolation)

• Time advancement– 3rd order, low memory Runga-Kutta

• Equation of state– tabular – including ionization, excitation– H, He + abundant elements

• Radiative transfer– 3D, LTE– 4 bin multi-group opacity

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Simulation set up

• Vertical boundary conditions: Extrapolate lnρ; Velocity -> constant @ top, zero derivative @ bottom; energy/mass -> average value @ top, extrapolate @ bottom;

• B tends to potential field @ top,• Horizontal Bx0 advected into domain by inflows

@bottom (20 Mm), 2 cases: Bx0 = 5 & 20kG• f-plane rotation, latitude 30 deg• Initial state – non-magnetic convection.

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Mean Atmosphere

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Total Unsigned Vertical Flux (48x48 Mm) at τcont = 1

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ΙBΙ & Velocity

Flux Emergence20 kG case, 15 – 32 hrs

Average fluid rise time = 32 hrs (interval between frames =1 min) 96 km horizontal resolution -> 48 km

Bv Bh

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EmergentIntensity,I/<I>

Flux Emergence(20 kG case)

32.1-34.2 hrs(interval betweenframes =1 min)

Horizontal resolution24 km.

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VerticalMagneticField

Pore/Spot Development(20 kG case)

32.1-34.2 hrs(interval betweenframes =1 min)

Horizontal resolution24 km.

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Magnetic Field (kG)

scan in

depth

t=34.2 hrs

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Magnetic Field Distribution @ τ = 0.1

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Intensity Distribution

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Emergent

Intensity

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Vertical Velocity (blue/green up, red/yellow down) & Magnetic Field lines(slice at 5 Mm)

vertical B -> velocity suppression

weak & horizontal B-> normal granulation

weak & horizontal B-> normal granulation

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Detail

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Stokes Profiles

Pore

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I V

Q U

V: simulation (left) & Hinode psf (right)(6302.4 - 6302.6)

V line profiles from LILIAsolid=raw, dashed = + psf

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Waves in Hydro Convection

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Magnetic Field

Vertical Horizontal

Active Region

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Intensity Distribution

Active Region

Quiet Sun

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Velocity Distribution

Active Region

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Questions:• Currently rising magnetic flux is given the same

entropy as the non-magnetic plasma, so it is buoyant. What entropy does the rising magnetic flux have in the Sun? Need to compare simulations with observations for clues.

• What will the long term magnetic field configuration look like? Will it form a magnetic network? Need to run for several turnover times (2 days).

• What is the typical strength of the magnetic field at 20 Mm depth? Again, need to compare long runs with observations for clues.

• Do we need to go to larger horizontal dimensions?

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Location of Data• Slices at 1min. intervals of: Velocity & Magnetic

Field, at τcont = 1, 0.1, 0.01. + Emergent Intensity, @ http://steinr.pa.msu.edu/~bob

• 4 hour averages at 2 hour cadence of:sound speed, temperature, density, velocity (3 directions), magnetic field (3 components)@ steinr.pa.msu.edu/~bob/mhd48-20/AVERS4hr

• Raw data cubes, averages & slices: all athttp://jsoc.stanford.edu/ajax/lookdata.html(Hydro 48 Mm & 96 Mm, MHD eventually)